Why buy insurance?

I don’t understand why people buy insurances when they know that odds are is not their favor. Is it not better bet to stay uninsured, and save money? I am not talking about house insurance. About things of which cost can be covered by one. Laptop, phone etc.

23 thoughts on “Why buy insurance?

  1. Cort Ammon

    People’s value of money is not always linear. Consider an individual with $1000 in the bank. I’m going to look at amounts of debt by orders of magnitude:

    • If something happens that costs $100, the situation can be resolved simply by giving someone 100 slips of green paper. This has little impact on their lives, besides decreasing their net worth by 10%.
    • If something happens that costs $1000, the situation can be resolved by giving someone 1000 slips of green paper. Now this starts to push on the individual ability to buy life needs, like groceries.
    • If something happens that costs $10,000, the situation may require a line of credit. Now there’s the question of interest, which has an exponential effect. By the time all is said and done, this may cost $30,000 or more due to interest payments.
    • If something happens that costs $100,000, now the individual has no monetary way of solving the problem. Now we enter the world of lawsuits, collections, arrest warrants, and all sorts of things.

    Now its pretty easy to see a order of magnitude increase in impact from $100 to $1000, and it becomes slightly worse for the $10,000 case due to debt. However, one more order of magnitude, going to $100,000, and suddenly it becomes hard to argue that there’s a mere “order of magnitude more hurt” than the $10,000 case. From the cases I’ve read, those sorts of situations can be far far worse than the monetary cost could convey.

    Insurance companies are in a good position to absorb $100,000 of debt if something happens, far better position than the individual. They rely on the central limit theorem: in general, they don’t have to pay out all at once.

    The insurance companies have their limits too. When hurricane Katrina came through, the insurance companies had a tremendously difficult time dealing with so many claims all at once. Just like the individuals, they found a sudden change in how much value they had to put on their monetary debts!

  2. Shep

    The fundamental flaw here is conflating net worth with utility, at least failing to recognize that there’s a nonlinear relationship between the two.

    • In the extreme example imagine taking a bet that will either make you twice as rich or completely broke. Your expected return is zero, but it would be pretty dumb to take it since being flat broke could ruin your life while being twice as rich may only improve it marginally.

    • In more realistic cases most of your income is tied up in fixed costs, which magnifies relatively small perturbations to your net worth. Losing something essential (like your house or car), even if it’s only 20% of your net worth, renders you effectively broke until you scrape together enough cash to get another one. That situation robs you of much more utility than you’d gain from a 20% increase in net worth.

    In either case, avoiding the risk is completely rational as long as you believe in nonlinear utility as a function of net worth, it’s not just an issue of humans being “risk averse”.

  3. user1944408

    This is just an addition to base64’s answer.

    In order to maximize your overall wealth (and wellbeing) in a long run, it is not enough to look only at the expected value (EV).

    In his example of always keeping $9850 or having $10000 99% of the time, EV in the second case is greater ($9900 > $9850) and if you are Bill Gates than you should not take an insurance in this case. But if your wealth is a lot less than that you should take an insurance.

    Take a look at Kelly criterion and utility functions. If I offer you to take 100 million dollars (no strings attached) or to take a risk to get 200 million dollars 60% of the time (and $0 40% of the time), would you take that risk? You shouldn’t but Bill Gates should take that risk because that would be a very good investment for him.

    Utility functions can help you choose if you want an insurance or not. Maybe you want to insure your house because the value of the house is a large percentage of your wealth but on the other hand you don’t need to insure your car if it is very easy for you to afford another one (but not easy to afford another house).

    Lets calculate what your wealth should be in order not to take this $150 insurance on a $10000 item. If you pay $150 for an insurance you have guaranteed $9850. But choosing not to take an insurance is the same as betting $9850 in order to gain $150 99% of the time. By using Kelly criterion formula fraction of the wealth needed to make this bet is: [p*(b+1)-1]/b = [0.99*(150/9850+1) -1]/ (150/9850) = 1/3.
    That means that if your wealth greater than $29950 you don’t need an insurance. But if you want to be sure it is advised to use fractional Kelly betting (for example you could multiply fraction by 1/2) and in that case if your wealth is more than $59900 you don’t need an insurance for this item.

  4. unknownprotocol

    The definition of insurance is the transfer of risk.

    Thus, you’re paying for transferring of a risk (of an item/property) to the insurer (carrier), so that they bear the financial burden of a loss/accident and not you.

    You could always self-insure, but a lot of times, insurance is cheaper, since due to the “Law of Large Numbers” the insurer can just charge a premium that is small percentage in comparison to the cost of self-insuring.

  5. AJ Henderson

    As someone who has worked for both an insurance carrier and an insurance agent, the reason people buy insurance is two fold: to spread risk out, and to get the benefits (when applicable) of approaching risk as a group.

    What you are really doing when you buy insurance is you are buying in to a large group of people who are sharing risk. You put money in that will help people when they take a loss, and in exchange get a promise of having your losses covered. There is an administrative fee taken by the company that runs the group in order to cover their costs of doing business and their profits that they get for running the group well (or losses they take if they run it poorly.)

    Some insurances are for profit, some are non-profit; all work on the principle of spreading risk around though and taking risk as a larger group.

    So let’s take a closer look at each of the advantages you get from participating in insurance. The biggest and most obvious is the protection from catastrophic loss. Yes, you could self-insure with a group size of one, by saving your money and having no overhead (other than your time and the time value of your money) but that has a cost in itself and also doesn’t cover you against risk up front if you aren’t already independently wealthy. A run of bad luck could wipe you out entirely since you don’t have a large group to spread the risk around. The same thing can still happen to insurance companies as well when the group as a whole takes major losses, but it’s less likely to occur because there are more rare things that have to go wrong. You pay an administrative overhead for the group to be run for you, but you have less exposure to your own risks in exchange for a small premium.

    Another significant but less visible advantage is the benefit of being part of a large group. Insurance companies represent a large group of people and lots of business, so they can get better rates on dealing with recovering from losses. They can negotiate for better health care rates or better repair rates or cheaper replacement parts. This can potentially save more than the administrative overhead and profit that they take off the top, even when compared to self-insuring.

    There is an element of gambling to it, but there are also very real financial benefits to having predictable costs. The value of that predictability (and the lesser need for liquid assets) is what makes insurance worth it for many people.

    The value of this group benefit does decrease a lot as the value of the insurance coverage (the amount it pays out) decreases. Insurance for minor losses has a much smaller impact on liquidity and is much easier to self insure. Cheaper items that have insurance also tend to be high risk items, so the costs tend to be very high relative to the amount of protection.

    If you are financially able, it may make more sense to self-insure in these cases, particularly if you tend to be more cautious. It may make sense for those who are more prone to accidents with their devices to buy insurance, but this selection bias also drives the cost up further.

    Generally, the reason to buy insurance on something like a cellphone is because you expect you will break it. You are going to end up paying for an entire additional phone over time anyway and most such policies stop paying out after the first replacement anyway.

    The reason why people buy the coverage anyway, even when it really isn’t in their best interest is due to two factors: being risk averse, as base64 pointed out, and also being generally bad at dealing with large numbers. On the risk averse side, they think of how much they are spending on the item (even if it is less compared to large items like cars or houses) and don’t want to lose that. On the bad at dealing with large numbers side, they don’t think about the overall cost of the coverage and don’t read the fine print as to what they are actually getting coverage for. (This is the same reason that you always see prices one cent under the dollar.)

    People often don’t really subconsciously get that they are paying more even if they would be able to eat the loss, so they pay what feels like a small amount to offset a large risk. The risk of loss is a higher fear than the known small, easy payment that keeps the risk away and the overall value proposition isn’t even considered.

  6. Five Bagger

    First of all, insurance never covers the cost of the item, it is almost always a partial payout at best. For example, a typical house in the Northeast US where I live that costs $300,000 will have the actual house valued at maybe $100,00 and rest of the value will be in the land. Therefore, the insured value will typically be $100,000. The only problem is that to actually rebuild the house might easily cost $250,000. So, your idea that some kinds of insurance allows the beneficiary to recoup their loss is usually never true.

    As you say, from an actuarial point of view insurance is a sheer waste of money. For example, a typical house has maybe a 0.5% chance of burning down every year. In other words out of 2000 houses, maybe 1 will burn down every year. So, lets say you got $100,000 of insurance on your house. Then the value of that policy would be $100,000 / 2000 = $50 per year. An insurance company will charge around $700 per year for the policy. That means you are basically flushing $650 down the toilet every year to maintain that policy.

    The reason why they do this is what blankip says above, they are buying “peace of mind”, a psychological product. In other they imagine they are somehow safe. So, even though they are losing money, paying it makes them feel as though they are not losing money. It’s delusional, but then again most people have a lot of delusions of which insurance is just one of many.

  7. blankip

    Insurance is bought for peace of mind and to divert disaster.

    Diverting disaster is a good/great thing. If your house burned down, if someone hit your car, or some other devastating event (think medical) happened that required a more allocation than you could afford the series of issues may snowball and cause you to lose a far greater amount of money than the initial incident. This could be in the form of losing work time, losing a job, having to buy transportation quickly paying a premium, having to incur high rate debt and so on.

    For the middle income and lower classes medical, house, and medical insurance certainly falls into these categories. Also why a lot of states have buyout options on auto insurance (some will let you drive without insurance by proving bonding up to 250K.

    Now the other insurance as I have alluded to is for peace of mind mainly. This is your laptop insurance, vacation insurance and so on. The premise of these insurances is that no matter what happens you can get back to “even” by paying just a little extra.

    However what other answers have failed to clarify is the idea of insurance. It is an agreement that you will pay a company money right now. And then if a certain set of events happen, you follow their guidelines, they are still in business, they still have the same protocols, and so on that you will get some benefit when something “disadvantageous” happens to you. We buy insurance because we think we can snap our fingers and life will be back to normal. For bigger things like medical, home, and auto there are more regulations but I could get 1000 comments on people getting screwed over by their insurance companies. For smaller things, almost all insurance is outsourced to a 3rd party not affiliated legally with a business. Therefore if the costs are too high they can simply go under, and if the costs are low they continue helping the consumer (that doesn’t need help).

    So we buy insurance divert catastrophe or because we have fallen for the insurance sales pitch. And an easy way to get around the sales pitch – as the person selling you the insurance if you can have their name and info and they will be personally liable if the insurance company fails their end of the bargain.

  8. Jasper

    Lots of people make poor decisions in crises. Some panic, and don’t make any decision at all.

    Insurance for affordable things can provide emotional security: If something goes wrong, the purchaser will not have to make a painful financial decision in a crisis. Many people do not want to have the burden of arguing about money, or having to spend precious cash, or borrow money, or raid savings accounts, just at the time they are already reeling from another loss. Having insurance “just take care of it” can save them an emotional double-whammy.

    Several kinds of insurance fill this perceived need:

    • Dental insurance. If you have a serious tooth-ache, do you want the fear of the full cost of a root canal to discourage you from getting it taken care of?
    • Comprehensive automobile insurance. Even if your car is old and cheap, do you want to have to worry about the cost to fix or replace it when you have just survived an accident? or discovered it stolen?
    • AAA. It’s nice having a superhero on speed-dial.
    • Jewelry insurance. If your wife breaks her diamond, do you really want an argument about how to find the money to replace it?
    • Phone theft/breakage insurance. If your phone gets smashed, wouldn’t you like to just make a call, and have it taken care of? Shopping for a new phone while your old phone is out of commission might not be a pleasant experience.
    • Pre-paid funeral services. If you make all of your final arrangements ahead of time, your funeral can be the way you want it to be. Your grieving relatives don’t need to worry about how expensive the funeral home is — you have taken care of those choices. (Plus, pre-paid funeral services don’t suffer the delays of probate and ordinary life insurance policies.)
  9. Dancrumb

    Discussions around expected values and risk premiums are very useful, but there’s another thing to consider: cash flow.

    Some individuals have high value assets that are vital to them, such as transportation or housing.

    The cost of replacing these assets is prohibitive to them: their cashflow means that their rate of saving is too low to accrue a fund large enough to cover the asset’s loss.

    However, their cashflow is such that they can afford insurance. While it may be true that, over time, they would be “better off” saving that money in an asset replacement fund, until that fund reaches a certain level, they are unprotected.

    Thus, it’s not just about being risk averse; there are some very pragmatic reasons why individuals with low disposable income might elect to pay for insurance when they would be financially better off without it.

  10. supercat

    There are many situations where injecting a certain amount of cash at the right time may reap rewards far in excess of the value of the cash injected.

    For example, if someone who needs a car to get to work gets in a wreck and that person does not have ready money to make it driveable may have no choice but to secure very expensive financing. Receipt of $1000 in ready money to repair the car may thus save the person from having to take out a loan that would cost $1200 or more to repay.

    While the insurance business has sufficient overhead that it is unlikely that insurance would generally have a positive net expectation even considering such factors, it is at least theoretically possible that insurance could have a positive expected value for both the insurer and the insured (and in some cases it may have positive expected values for both parties in practice as well).

  11. Verdant

    I keep it simple. Here’s what I learned when I took Personal Financial Planning: Insurance is for low likelihood, high-impact events.

  12. Nathan L

    There are several insurance products that I buy for legal reasons:

    • Homeowners insurance
    • Auto insurance

    Both of these protect me from lawsuits and fines. Many people buy similar products to protect their business operations. (e.g. medical malpractice insurance)

    There are some insurance products I buy for tax planning and financial planning purposes:

    • Life insurance
    • Medical insurance

    I have a large amount of savings available, so I have several tricks to reduce my insurance costs, and I have several products that I avoid.

    • I keep high deductibles on policies
    • I don’t buy vision or dental insurance
    • I don’t pay for extended warranties

    Several of these reasons are mentioned in other answers, but I thought I would collect them into a single answer to demonstrate that there are reasons other than the rational calculation of what the payout will be for the insurance products vs. the premium paid. If I gain access to a tax advantaged Health savings account, that is a bigger benefit to me than avoiding the premium, especially when my employer is paying the majority of the premium. Perhaps it makes no sense to buy insurance given sufficient savings (like the products I listed that make no sense for me given my finances) but not everyone can self-insure; it does require a certain level of wealth.

  13. Ian

    Apart from legal requirements to have insurance, e.g. 3rd party car that other answers have covered well.

    We can think of all insurance as protecting our “usable” income, as we can use cashflow to pay the costs of a loan to replace whatever we decided not to insure. So for example, if I don’t insure my house contents, I can replace them on my credit card if needed.

    Therefore we are paying for insurance out of our income, so as to protect our income, knowing that the cost of the protection is on average more than the benefit we get from it.

    But we all know that having an income of $50K is less than double the value of having an income of $25K. (E.g. being able to eat and remain warm is more important to us then being able to go on anther holiday.) This is way when someone has a higher income; it requires more money to effect their actions.

    Loss aversion is another factor; we are people not logistical machines.

  14. user33793

    Most people buy insurance because it is legally required to own a car or to have a mortgage. People want to own homes and to have personal transportation enough that they are willing to pay for required insurance costs.

    There are a lot of great explanations here as to why insurance is important and I don’t want to detract from those at all. However, if we’re being honest, most people are not sophisticated enough to measure and hedge their various financial risks. They just want to own an home and to drive a car.

  15. Hurkyl

    The odds could very well be in your favor, even when the insurance company expects profit.

    What matters to you is not the expected amount of money you’ll have, but the expected amount of utility you’ll get from it: getting enough money to buy food to eat is much more important than getting enough money to be able to buy that fiction book too.

    The more money you have, the less a dollar is worth to you: consequently, if you have enough money, it’s worth spending some to prevent yourself from getting into a situation where you don’t have enough money.

  16. Zenadix

    One reason is that insurance gives you tranquility.

    Without insurance, you live with the uncertainty of not knowing if/when disaster is going to strike.

    Insurance allows you to trade this uncertainty for regular monthly/yearly payments.

  17. BrenBarn

    You don’t mention what kind of insurance you’re talking about, but I’ll just address one angle on the question.

    For some kinds of insurance, such as health insurance (in the US), auto insurance, and homeowner’s insurance, you may be insuring against an event that you would not be able to pay for without the insurance. For instance, if you are at fault in a car accident and injure someone, they could sue you for $100,000. A lot of people don’t have $100,000. So it’s not even a matter of “I’ll take the risk of having to pay it when the time comes”; if the time comes, you could lose virtually everything you own and still have to pay more from future earnings. You’re not just paying $X to offset a potential loss of $Y; you’re paying $X to offset a potential derailment of your entire life. It is plausible that you could assign a reasonable monetary value to that potential “cost” that would mean you actually come out ahead in the insurance equation.

    It is with smaller expenses (such as insuring a new cellphone against breakage) that insurance becomes harder to justify. When the potential nonfinancial “collateral damage” of a bad event are less, you must justify the insurance expenses on the financial consequences only, which, as you say, is often difficult.

  18. Kent A.

    There’s an old saying among commodities producers… If it’s likely to happen, but won’t kill you, you hedge (save/”self-insure”, options, futures). If it’s not likely to happen, but would kill you, you insure.

    Hedging and insuring are both about managing risk. If you feel there is no risk at all, you don’t need to do either. But feeling that you have no risk at all is somewhat naive.

  19. nwp

    For big values the loss becomes negligible. Say you have a 10% chance to get 10 million $/€/Whatever, expected value 1m. You sell that chance for 990k, which loses you 10k of expected income. Why would you throw away 10k? Because in the face of getting almost 1m the 10k are insignificant, 1m and 990k will make you roughly equally rich. Also the richness increase from 1m to 10m is less than 10x since 1m gives you maybe 90% of the freedom that 10m does (depending on how well you can make 10m work for you, most people will just let it rot in the bank).

    Another way to look at it is to look at bankruptcy risk. Say I have 10k in the bank, which is nice. Those 10k cannot pay for a new house or 2 cars (mine and the one I hit), so I have a small risk of significant loss. If I buy an insurance I reduce my chance of going bankrupt from maybe 0.001% to 0% for a fairly small price. Usually you can buy insurance fairly cheap if you raise your deductible to maybe 5k (both for the house and the car) so that you shoulder the risk you can (shouldering risk = gaining money) and paying an insurance to shoulder the rest for you. That way you minimize the cost to remove the risk of bankruptcy. It makes sense to shoulder as much risk as you can (unless a fixed fee of the insurance makes in unfeasible) before paying others to do it for you so you can optimize your income while removing fatal risks.

  20. base64

    Because people are Risk Averse.

    Suppose that you own an asset worth $10,000 to you.

    Suppose that each year, the asset has 1% chance of being stolen (or completely broken).

    The expected value is 99% x 10,000 + 1% x $0 = $9,900. This is the average outcome if you do not buy insurance.

    Now consider two mutually exclusive outcomes:

    1. 99% chance of keeping $10,000 and 1% chance of losing everything
      (expected value: $9,900)

    2. 100% chance of keeping $9,900 (expected value: $9,900)

    Everyone would choose option 2, even though the expected values are the same.

    Option 2 is an insurance that cost $100 (Actuarially fair, aka the odds are fair).

    Now suppose the insurance costs $150 instead of $100 (despite that the bad probability is still 1%). You are faced with

    1. 99% chance of keeping $10,000 and 1% chance of losing everything
      (expected value: $9,900)

    2. 100% chance of keeping $9,850 (expected value: $9,850)

    Some people would still choose option 2, even though the expected value is actually lower.

    The $50 is called Risk Premium, which people are willing to pay in order to avoid uncertainty. The odds are unfair, but the Risk Premium has its value.

    That being said, competition between insurance companies would drive down the premium until the insurance is close to actuarially fair, but they have cost to cover (sales, administration, etc), making the odds “unfair”.

  21. mhoran_psprep

    Regarding auto insurance, you have to look at the different parts.

    In the United Sates most states do require a level of specific coverage for all drivers. That is to make sure that if you are at fault there is money available to pay the victims. That payment may be for damage to their car or other property, but it also covers medical costs. Many policies also cover you if the other driver doesn’t have insurance.

    The policy that covers the loss of the vehicle is required if you have a loan or are leasing the car. Somebody else owns it while there is a loan, so they can and do require you to pay to protect the vehicle. If there i no loan you don’t have to have that portion of a policy.

    Other parts such as towing, roadside assistance, and rental cars replacement may be required by the insurance standards for your state, or might be almost impossible to drop because all insurance companies include it to stay competitive with their competition.

    Dropping the non-required parts of the coverage is acceptable when you don’t have a loan. Some people do drop it to save money. But that does mean you are self insuring. If you can afford to self insure a new car, great.

    The interesting thing is that some people have more than enough assets to self inure the non-required part of auto insurance. But then they realize that they do need to up their umbrella liability insurance. This is to protect them from somebody deciding that their resources make them a tempting target when they are involved in a collision.

  22. JoeTaxpayer

    (Disclosure – I am a real estate agent, involved with houses to buy/sell, but much activity in rentals)

    I got a call from a man and his wife looking for an apartment. He introduced itself, described what they were looking for, and then suggested I google his name. He said I’d find that a few weeks back, his house burned to the ground and he had no insurance. He didn’t have enough savings to rebuild, and besides needing an apartment, had a building lot to sell.

    Insurance against theft may not be at the top of your list. Don’t keep any cash, and keep your possessions to a minimum. But a house needs insurance for a bank to give you a mortgage. Once paid off, you have no legal obligation, but are playing a dangerous game. You are right, it’s an odds game. If the cost of insurance is .5% the house value and the chance of it burning down is 1 in 300 (I made this up) you are simply betting it won’t be yours that burns down.

    Given that for most people, a paid off house is their largest asset, more value that all other savings combined, it’s a risk most would prefer not to take.

    Life insurance is a different matter. A person with no dependents has no need for insurance. For those who are married (or have a loved one), or for parents, insurance is intended to help survivors bridge the gap for that lost income. The 10-20 times income value for insurance is just a recommendation, whose need fades away as one approaches independence. I don’t believe in insurance as an investment vehicle, so this answer is talking strictly term.

  23. littleadv

    It’s not a betting game, insurance policy is not akin to a casino bet.

    While the odds are probably low, the damage of an event may be devastating. Insurance allows mitigating that potential devastating damage, if it occurs.

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